Sharp Hardy-Leray inequality for three-dimensional solenoidal fields with axisymmetric swirl
Abstract
In this paper, we prove Hardy-Leray inequality for three-dimensional solenoidal (i.e., divergence-free) fields with the best constant. To derive the best constant, we impose the axisymmetric condition only on the swirl components. This partially complements the former work by O. Costin and V. Maz'ya Costin-Mazya on the sharp Hardy-Leray inequality for axisymmetric divergence-free fields.
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